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Popular >

integral of (2-x)/x

Solution

\int \frac{2 - x}{x} d x

Solution

2 ln ∣ x ∣ - x + C

Solution steps

\int \frac{2 - x}{x} d x

Expand

\frac{2 - x}{x} : \frac{2}{x} - 1

= \int \frac{2}{x} - 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{2}{x} d x - \int 1 d x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int 1 d x = x

= 2 ln ∣ x ∣ - x

Add a constant to the solution

= 2 ln ∣ x ∣ - x + C

Graph

Popular Examples

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\int x^{2} d x

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n = 1 \sum \infty \frac{n !}{2 n ! + 1}

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\int - 14 sin (x) d x

laplacetransform 2(e^{-t}-1)+t(e^{-t}+1)laplace transform

2 (e^{- t} - 1) + t (e^{- t} + 1)

derivative of arctan(cos(8x))

\frac{d}{d x} (arctan (cos (8 x)))

Frequently Asked Questions (FAQ)

What is the integral of (2-x)/x ?
The integral of (2-x)/x is 2ln|x|-x+C